1010 [HNOI2008]玩具装箱toy

斜率优化dp；

推荐学习http://www.cnblogs.com/perseawe/archive/2012/05/12/bz1010.html

看着别人的题解自己学着推，终于理解了

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define maxn 50005
using namespace std;

int q[maxn],head=0,tail=0;
ll f[maxn];
ll g[maxn],s[maxn];
ll dp[maxn];

ll get_g(int k,int j,int c)
{
    return dp[k]+(f[k]+c)*(f[k]+c)-dp[j]-(f[j]+c)*(f[j]+c);
}

ll get_s(int k,int j)
{
    return 2*(f[k]-f[j]);
}

int main()
{
    int n,m,xx;
    scanf("%d%d",&n,&m);
    for(int i=1; i<=n; i++)
    {
        scanf("%d",&xx);
        f[i]+=f[i-1]+xx;
    }
    for(int i=1; i<=n; i++)f[i]+=i;
    int c=1+m;
    q[tail++]=0;
    for(int i=1;i<=n;i++)
    {
        while(head<tail-1&&get_g(q[head+1],q[head],c)<=f[i]*get_s(q[head+1],q[head]))++head;
        int v=q[head];
        dp[i]=dp[v]+(f[i]-f[v]-c)*(f[i]-f[v]-c);
        q[tail++]=i;
        for(int j=tail-2;j>head;j--)
        {
            int cc=q[j+1];
            int bb=q[j];
            int aa=q[j-1];
            if(get_g(bb,aa,c)*get_s(cc,bb)>=get_g(cc,bb,c)*get_s(bb,aa))
                q[j]=q[--tail];
            else break;
        }
    }
    printf("%lld\n",dp[n]);
    return 0;
}

View Code

 

转载于:https://www.cnblogs.com/yours1103/p/3453985.html